An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension.
The most common use of an augmented matrix is in the application of Gaussian elimination to solve a matrix equation of the form
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(1)
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by forming the column-appended augmented matrix
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(2)
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Augmented matrices can also be used to find a matrix inverse of 
by forming
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(3)
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with 
the identity matrix of appropriate dimension,
then using elementary row operations to reduce the result to the form
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(4)
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The payoff matrix in game theory is a case of a more complicated augmented matrix .
